Why are bash brace expansions not working for commands?

Your brace expansion is not valid. A brace expansion must be one word in the shell.

A word is a string delimited by unquoted spaces (or tabs or newlines, by default), and the string {chown httpd,chmod 700} consists of the three separate words {chmod, http,chmod and 700} and would not be recognised as a brace expansion.

Instead, the shell would interpret the line as a {chown command, executed with the arguments http,chmod, 700} and /dir/test1.

The simplest way to test this is with echo:

$ echo {chown httpd,chmod 700} /dir/test1
{chown httpd,chmod 700} /dir/test1

$ echo {"chown httpd","chmod 700"} /dir/test1
chown httpd chmod 700 /dir/test1

Note that even if your brace expansion had worked, the command would have been nonsensical.

Just write two commands,

chown http /dir/test1
chmod 700  /dir/test1

because, as mentioned in the man page, bash will perform the brace expansion on each word after splitting a command line into words.

So, that command line will be first split into {chown, httpd,chmod and 700}, and then, since {chown is not a valid brace expansion pattern, it will be left as is and bash will try to run a command with that name.

This is the quote from the manpage:

Expansion is performed on the command line after it has been split into words. There are seven kinds of expansion performed: brace expansion, tilde expansion, parameter and variable expansion, command substitution, arithmetic expansion, word splitting, and pathname expansion.

Notice the order, which is different from other shells (in zsh, the brace expansion will be performed after the arithmetic expansion, and the extra word splitting won't be performed at all).

The following will print 1 2 in zsh or ksh, and x y in bash:

f=; f1=x; f2=y; echo $f{1,2}